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lecture7 - Microeconomics I Lecture#7 7 7.1 The Optimum of...

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Microeconomics I - Lecture #7, March 31, 2009 7 The Optimum of Monopoly, Price Discrimination 7.1 Monopoly Up to now we have analyzed the behavior of a competitive industry, a market structure that is most likely when there are a large number of small firms. In that case all firms took price as given. In this chapter we turn to the opposite extreme and consider an industry structure when there is only one firm in the industry-a monopoly. A monopolist does not take the price as given. The monopolist will choose the price to maximize the profit. Profit maximization: Recall, that in case of perfect competition the optimality condition is MR = MC . In case of perfect competition marginal revenue is equal to price and hence in the optimum price equals marginal cost ( p = MC ). This holds because in perfect competition firms take price as given and hence the price is not function of output y . However, in case of monopoly the price is a function of output (the higher the price the lower the demand and vice versa) and hence the term for marginal revenue is a little more complicated. Let’s use p ( y ) to denote the market inverse demand curve and c ( y ) to denote the cost function. Let r ( y ) = p ( y ) y denote the revenue function of the monopolist. The monopolist’s profit-maximization problem then takes the form max y r ( y ) - c ( y ) = max y p ( y ) y - c ( y ) Optimality condition: at the optimal choice of output we must have marginal revenue equal to marginal cost ( MR = MC or p 0 ( y ) y + p ( y ) = c 0 ( y )). If marginal revenue were less than marginal cost it would pay the firm to decrease output, since the savings in cost would more than make up for the loss in revenue. If the marginal revenue were greater than the marginal cost, it would pay the firm to increase output. The only point where the firm has no incentive to change output is where marginal revenue equals marginal cost. Another way to think about this is to think of the monopolist as choosing its output and price simultaneously. If the monopolist wants to sell more output it has to lower its price. But this lower price will mean a lower price for all of the units it is selling, not just the new units. In the competitive case, a firm that could lower its price below the price charged by other firms would immediately capture the entire market from its competitors. But in the monopolistic case, the monopoly already has the entire market; when it lowers its price, it has to take into account the effect of the price reduction on all the units it sells.
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